Calculations of various integral parameters of branching transport processes (neutron counts, ionisation yield, number of defects, sputtering yield) show widely varying relative variances, such that both deeply sub-Poisson and highly over-Poisson types (even diverging ones) can occur. To understand and explain the reasons for such varied behaviour in apparently similar transport processes, the correlation structure, i.e. two-point density functions, were calculated for sputtering and defect creation, both in infinite media and half-spaces whenever applicable. The calculations were made by constant cross sections and hard-sphere scattering, employing the Khinchin-Pease damage model. It was shown that in addition to the sputtering yield, also the vacancy and interstitial yields have a highly over-Poisson variance in a half-space. The energy and spatial structure of the two-point correlations was investigated by Monte-Carlo calculations. Large positive correlations exist in the energy and depth of origin of sputtered particles. Defect correlation functions have a more complicated structure. Correlations in semi-infinite and infinite media show that the two parts of the cascade in infinite medium, separated by the injection point of the initial particle, develop nearly exclusive and independent of each other. The correlation functions presented illuminate the intrinsic laws governing the yield variances, and give some further interesting insight into the cascade dynamics.